Related papers: The inverse cyclotomic Discrete Fourier Transform …

This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…

We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…

In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…

In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.

An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…

We present here algorithms for efficient computation of linear algebra problems over finite fields.

In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.

We explore a new form of DFT, which we call the Polynomial Transform. It functions over finite fields, and a size $n$ transform takes $O(n)$ operations. In the multitape Turing machine model, it allows us to multiply two $n$ bit numbers in…

A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…

We give an overview over several constructions of TQFT's over finite fields and cyclotomic integers and their applications to characterizing 3-manifolds and their fundamental groups.

We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.

A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…

We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new…

Let $\mathbb{F}_q$ be the finite field of order $q$ and $F=\mathbb{F}_q(x)$ the rational function field. In this paper, we give a characterization of the cyclotomic function fields $F(\Lambda_M)$ with modulus $M$, where $M \in…

The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…

We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.

We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…

We prove an upper bound for the number of cyclic transitive subgroups in a finite permutation group and clarify the structure of the groups for which this bound becomes sharp. We also give an application in the theory of number fields.

Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier…